document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=287851>Question 287851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ten pennies and ten nickels were arranged alternatively as PNPN...PN. A move consists of exchanging the position of two adjacent coins. What is the minimum number of moves needed  to move all the pennies to one end,and all the nickels to the other end,i.e.,PPP...PN...NNN?\r<BR>\n" );
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document.write( "A 10    B 20   C 25   D 40   E 45 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #208645 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=208645\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To understand this question it is helpful to look at smaller cases:<BR>\n" );
document.write( "2 coins: pn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0 moves<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "3 coins:pnp -> ppn . . . . . . . . . . . . . . . . . . . . . . . 1 move<BR>\n" );
document.write( "4 coins:pnpn -> ppnn. . . . . . . . . . . . . . . . . . . . . . 1 move<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "5 coins:pnpnp -> ppnnp -> ppnpn -> pppnn . . . 3 moves<BR>\n" );
document.write( "6 coins:pnpnpn . . . . . . . . . . . . . . . . . . . . . . . . . . .3 moves<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "7 coins: pnpnpnp. . . . . . . . . . . . . . . . . . . . . . . . . . 6 moves<BR>\n" );
document.write( "8 coins: pnpnpnpn. . . . . . . . . . . . . . . . . . . . . . . . . 6 moves<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "9 coins: pnpnpnpnp. . . . . . . . . . . . . . . . . . . . . . . . .10 moves<BR>\n" );
document.write( "10 coins: pnpnpnpnpn. . . . . . . . . . . . . . . . . . . . . . .10 moves<BR>\n" );
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document.write( "Notice that the number of moves for each pair after the first will be triangular in nature: 0, 1,3,6,10 and so on.<BR>\n" );
document.write( "So, 10 pennies will have 10 moves; ( A ) </SPAN>\n" );
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